Molecular-Brownian Correspondence in the Hard-sphere Dynamic Universality Class

TL;DR

This study demonstrates that the dynamic behavior of soft-sphere liquids is fundamentally equivalent to that of hard-sphere liquids, regardless of microscopic laws, and extends this equivalence to compare Brownian and atomic systems with similar interactions.

Contribution

The paper provides systematic simulation evidence that dynamic equivalence between soft-sphere and hard-sphere liquids is independent of microscopic dynamics and confirms a new equivalence between Brownian and atomic liquids.

Findings

Dynamic equivalence holds across different soft-sphere systems.

Equivalence is independent of Newtonian or Brownian dynamics.

Long-time dynamics of Brownian and atomic systems are comparable.

Abstract

We perform systematic simulation experiments on model systems with soft-sphere repulsive interactions to test the predicted dynamic equivalence between soft-sphere liquids with similar static structure. For this we compare the simulated dynamics (mean squared displacement, intermediate scattering function, {\alpha}-relaxation time, etc.) of different soft-sphere systems, between them and with the hard-sphere liquid. We then show that the referred dynamic equivalence does not depend on the (Newtonian or Brownian) nature of the microscopic laws of motion of the constituent particles, and hence, applies independently to colloidal and to atomic simple liquids. In addition, we verify another more recently-proposed dynamic equivalence, this time between the long-time dynamics of a Brownian fluid and its corresponding atomic liquid (i.e., the atomic system with the same interaction potential).